{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "# Student's t distribution\n",
    "\n",
    "For more information, see chapters 9 and 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import gamma, digamma\n",
    "from scipy.stats import t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\"\n",
    "plt.rcParams[\"axes.spines.right\"] = False\n",
    "plt.rcParams[\"axes.spines.top\"] = False\n",
    "plt.rcParams['text.latex.preamble'] = [r'\\usepackage{amsmath}']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "Student's t distribution is defined as an ensamble of normal distributions \"weighted\" by precision terms $\\tau$ that are Gamma-distributed. That is\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    p(x|\\mu, \\alpha, \\beta) &= \\int_0^\\infty \\mathcal{N}\\left(x |\\mu, \\tau^{-1}\\right)\\text{Gam}(\\tau|\\alpha, \\beta) \\ d\\tau \\\\\n",
    "    &= \\frac{\\beta^\\alpha}{\\Gamma(\\alpha)}\\left(\\frac{1}{2\\pi}\\right)^{1/2}\\left[b + \\frac{(x - \\mu)^2}{2}\\right]^{-a - 1/2} \\Gamma\\left(a + \\frac{1}{2}\\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Defining $\\nu = 2\\alpha$, $\\lambda = \\alpha/\\beta$ and rearranging, we obtain the final form of the distribution in the form\n",
    "\n",
    "$$\n",
    "    \\text{St}(x\\vert\\mu,\\lambda,\\nu) = \\frac{\\Gamma\\big((\\nu + 1)/2\\big)}{\\Gamma(\\nu/2)}\\left(\\frac{\\lambda}{\\pi\\nu}\\right)^{1/2}\\left[1 + \\frac{\\lambda(x - \\mu)^2}{\\nu}\\right]^{-(\\nu + 1)/2}\n",
    "$$\n",
    "\n",
    "* $\\nu$ is known as the degrees of freedom of the distribution;\n",
    "* $\\lambda$ is known as the precision of the distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "def students(x, mu, lmbda, nu):\n",
    "    \"\"\"\n",
    "    Generates a function that returns the value\n",
    "    of the pdf of a Student's-t distribution\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    x: float, np.array\n",
    "        Values to evaluate the pdf at\n",
    "    mu: float\n",
    "        The mean of the distribution\n",
    "    lmbda: float\n",
    "        The precision of the distribution\n",
    "    nu: float\n",
    "        The degrees of freedom of the distributino\n",
    "    \"\"\"\n",
    "    const = gamma(nu / 2 + 1 / 2) / gamma(nu / 2) * np.sqrt(lmbda / (np.pi * nu))\n",
    "    pdf = const * (1 + (lmbda * (x - mu) ** 2) / nu) ** (-nu / 2 - 1 / 2)\n",
    "    return pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu, lmbda= 0, 1\n",
    "\n",
    "xrange = np.linspace(-5, 5, 200)\n",
    "\n",
    "nus = [0.1, 1, 10]\n",
    "for nu in nus:\n",
    "    pdf = students(xrange, mu, lmbda, nu)\n",
    "    plt.plot(xrange, pdf, label=rf\"$\\nu={nu}$\");\n",
    "plt.title(r\"$\\mathrm{St}\"rf\"(x\\vert\\mu={mu}, \\lambda={lmbda}, \\nu)$\", fontsize=15)\n",
    "plt.legend(fontsize=11);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "source": [
    "## Estimating the value of a digamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "def bisection(f, x_low, x_up, tol=1e-5, max_its=1000):\n",
    "    diff = np.inf\n",
    "    nits = 0\n",
    "    while diff > tol:\n",
    "        if nits >= max_its:\n",
    "            raise ValueError(\"Root searching did not converge\")\n",
    "            \n",
    "        x_mid = (x_low + x_up) / 2\n",
    "        f_mid = f(x_mid)\n",
    "\n",
    "        if np.sign(f_mid) == 1:\n",
    "            x_up = x_mid\n",
    "        else:\n",
    "            x_low = x_mid\n",
    "\n",
    "        diff = np.abs(f_mid)\n",
    "        nits += 1\n",
    "        \n",
    "    return x_mid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Student's-t $a$ parameter estimation\n",
    "\n",
    "To take an $M$-step in estimating the parameters of student's-t distribution, we require to satisfy the equality\n",
    "\n",
    "$$\n",
    "    \\log a - \\psi(a) = \\frac{1}{N}\\big(N \\log\\mathbb{E}[\\tau] - \\mathbb{E}[\\log\\tau]\\big)\n",
    "$$\n",
    "\n",
    "More generally, we would like to find $a \\in\\mathbb{R}$ that satisfies\n",
    "\n",
    "$$\n",
    "   \\big(\\log a - \\psi(a)\\big) - b = 0\n",
    "$$\n",
    "\n",
    "for any given $b\\in\\mathbb{R}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import requests\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "apikey = os.environ[\"AVANTAGE_API\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://www.alphavantage.co/documentation/\n",
    "url = \"https://www.alphavantage.co/query\"\n",
    "symbol = \"TSLA\"\n",
    "params = {\n",
    "    \"function\": \"TIME_SERIES_DAILY_ADJUSTED\",\n",
    "    \"symbol\": symbol,\n",
    "    \"outputsize\": \"full\",\n",
    "    \"apikey\": apikey\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = requests.get(url, params=params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "stock = pd.DataFrame.from_dict(r.json()[\"Time Series (Daily)\"], orient=\"index\", dtype=float)\n",
    "stock.index = pd.to_datetime(stock.index)\n",
    "stock = stock.sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "stock_ret = stock.rename({\"5. adjusted close\": symbol}, axis=1)[symbol].pct_change().dropna()\n",
    "N = len(stock_ret)\n",
    "mu, sigma = stock_ret.mean(), stock_ret.std(ddof=1)\n",
    "N_stock = norm(loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xrange = np.linspace(stock_ret.min(), stock_ret.max(), 100)\n",
    "sns.distplot(stock_ret, kde=False, norm_hist=True);\n",
    "plt.plot(xrange, N_stock.pdf(xrange), label=\"Adjusted Normal\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Student's-t EM\n",
    "\n",
    "TO-DO: Add respective equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "class St:\n",
    "    def __init__(self):\n",
    "        pass\n",
    "        \n",
    "    def E_nu(self, X):\n",
    "        return (self.nu + 1) / (self.nu + self.lmbda * (X - self.mu) ** 2)\n",
    "    \n",
    "    def E_log_nu(self, X):\n",
    "        return digamma((self.nu + 1) / 2) - np.log((self.nu + self.lmbda * (X - self.mu) ** 2) / 2)\n",
    "    \n",
    "    def E_step(self, X):\n",
    "        return self.E_nu(X), self.E_log_nu(X)\n",
    "\n",
    "    @staticmethod\n",
    "    def nu_root(k, **kwargs):\n",
    "        f = lambda nu: (digamma(nu / 2) - np.log(nu / 2)) - k\n",
    "        return bisection(f, **kwargs)\n",
    "    \n",
    "    def expected_log_likelihood(self, X):\n",
    "        N = len(X)\n",
    "        E, E_log = self.E_step(X)\n",
    "        Q = (- N * np.log(2 * np.pi) / 2 + E_log.sum() / 2 + N * self.lmbda / 2\n",
    "             - self.lmbda * (E * (X - self.mu) ** 2).sum() / 2\n",
    "             + N * self.nu * np.log(self.nu / 2) - N * np.log(gamma(self.nu / 2))\n",
    "             + (self.nu / 2 - 1) * E_log.sum() - self.nu * E.sum() / 2)\n",
    "        \n",
    "        return Q\n",
    "    \n",
    "    def M_step(self, X):\n",
    "        E, E_log = self.E_step(X)\n",
    "        mu = (E * X).sum() / E.sum()\n",
    "        lmbda = 1 / (E * (X - self.mu) ** 2).mean()\n",
    "        \n",
    "        cst = 1 + E_log.mean() - E.mean()\n",
    "        nu = self.nu_root(cst, x_low=0, x_up=5)\n",
    "        \n",
    "        self.mu = mu\n",
    "        self.lmbda = lmbda\n",
    "        self.nu = nu\n",
    "    \n",
    "    def fit(self, X, tol=1e-5, maxiter=500):\n",
    "        self.mu, self.lmbda, self.nu = 1, 1, 1\n",
    "        # Change of the expected log likelihood\n",
    "        ell, delta_ell = -np.inf, np.inf\n",
    "        nits = 0\n",
    "        while np.abs(delta_ell) > tol:\n",
    "            if nits >= maxiter:\n",
    "                raise ValueError(\"EM did not converge\")\n",
    "                \n",
    "            new_ell = self.expected_log_likelihood(X)\n",
    "            delta_ell = np.abs(new_ell / ell - 1)\n",
    "            ell = new_ell\n",
    "            self.M_step(X)\n",
    "            \n",
    "            nits += 1\n",
    "            \n",
    "            \n",
    "        return self.nu, self.mu, np.sqrt(1 / self.lmbda)\n",
    "    \n",
    "    def pdf(self, x):\n",
    "        \"\"\"\n",
    "        Generates a function that returns the value\n",
    "        of the pdf of a Student's-t distribution\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        x: float, np.array\n",
    "            Values to evaluate the pdf at\n",
    "        mu: float\n",
    "            The mean of the distribution\n",
    "        lmbda: float\n",
    "            The precision of the distribution\n",
    "        nu: float\n",
    "            The degrees of freedom of the distributino\n",
    "        \"\"\"\n",
    "        const = gamma(self.nu / 2 + 1 / 2) / gamma(self.nu / 2) * np.sqrt(self.lmbda / (np.pi * self.nu))\n",
    "        pdf_x = const * (1 + (self.lmbda * (x - self.mu) ** 2) / self.nu) ** (-self.nu / 2 - 1 / 2)\n",
    "        return pdf_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.9437255859375, 0.001411772604642491, 0.02139341535631292)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "st = St()\n",
    "st.fit(stock_ret)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xrange = np.linspace(stock_ret.min(), stock_ret.max(), 300)\n",
    "sns.distplot(stock_ret, kde=False, norm_hist=True);\n",
    "plt.plot(xrange, N_stock.pdf(xrange), label=\"Adjusted Normal\")\n",
    "plt.plot(xrange, st.pdf(xrange), label=\"Adjusted St\")\n",
    "plt.legend(fontsize=12);"
   ]
  }
 ],
 "metadata": {
  "hide_code_all_hidden": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
